Fractals and Time, Part I: Not as Fluffy as You Think . . .

by Christopher Vitale

Fractals have a bad rap for a good reason – a lot of really cheezy, new-agey stuff has been written about fractals. But fractals are mathematical objects with rigorous applications that need to be separated from the fluffy stuff done in their name.

So it was with a great degree of trepidation that I approached Keri Welch’s dissertation, A Fractal Topology of Time, just completed at the California Institute for Integral Studies, which I hadn’t heard of before, but which sounded quite new-agey. But someone with strong cred in my book recommended it, and mentioned some of the concepts, and they sounded promising.

Well, let me just say that the work done in here is top notch, and really worth reading. Welch largely combines the work of three theorists – French theoretical cosmologist Laurent Nottale, German fractal researcher Susie Vrobel, and the inimitable Roger Penrose – to develop the most rigorous account of the potential relation between time and fractality that I’ve seen to date. This work is really a full on mixture of physics and philosophy, and seems to me to succeed in its endeavor.

While Welch does provide some context in regard to the philosophical tradition, and describes in detail at points certain concepts by Bergson, Husserl, and Whitehead, this is largely a work of philosophy of physics. The implications of her work in relation to continental theory and speculative realisms these days is not developed. But it hits me that there’s a LOT of potential here.

What follows is a summary and sketch of what that might look like. First, though, I need to explain what is meant by ‘timelessness’ in contemporary quantum physics discourse, because her task, as she articulates it, is to use fractals to show how “time can be generated from timelessness.” The rest of this post will do this set-up work, the next post will explain Welch’s work itself.

But first, here’s a bibliography that gives a sense of where I’m getting the claims I make in the next section:

– The End of Time: The Next Revolution in Physics, by Julian Barbour

– Before the Big Bang: The Prehistory of Our Universe, by Brian Clegg

– In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality, by John Gribben

What might it mean for time to be fractal? Firstly, we need to specify whether the time described is subjective or objective, and for Welch, the theories of Nottale, Vrobel, and Penrose allow us to think both, as well as potential relations between the two.

Welch distinguishes three levels of time familiar to all physicists, if not explicitly differentiated as such – linear time, reversible time, and timelessness. Linear time is the time that flows, in which A precedes B, and causes create effects who follow them in time, but there is no reverse causality.

However, many physicists have argued that many quantum phenomenon become comprehensible once we imagine the possibility of bi-directional or reverse causality. That is, unless causes and effects line up both forwards and backwards in time, an event won’t occur. Such an approach solves the apparent physical contradictions brought to light by famous quantum experiments such as the EPR experiment, or quantum erasers (and for more on these, see my post here).

Now if quantum phenomenon experience a ‘smearing’ of spacetime, and if our universe likely started with a Big-Bang-like event of some sort, then it seems likely that the entirety of our universe was squished into an incredibly small, dense packet of condensed spacetime in which quantum rules, such as superposition, time-reversal, spatial spreading, and self-interference apply.

From such a perspective, it might not be absurd to wonder if perhaps all possible universes that could emerge from the Big-Bang were all present, superimposed, condensed in time and space, and that our universe is simply the unfolding of one of these within the ‘extended’ (to use a Whiteheadian term) existence of spacetime which we know as existence in our universe. Of course, there’s no way to know if the universe is not in fact pursuing all of these simutaneously (a multi-verse interpretation of the cosmos), and if quantum ‘decisions’ create paths that leap between these or split and recombine these (‘multiple-worlds’ interpretation of quantum mechanics).

Some have even argued that our universe is a large hologram. Holograms don’t encode a 3D image in a 2D plane (ie: a photograph), but rather, the difference between a reference rays directed straight at a plane of glass and a rays directed from a multitude of angles at that glass after hitting an object. From this differential encoding, a hologram can reconstruct the virtual image of a 3D object from a 2D imprint.

From this we may begin to question – might not our whole universe not actually have left that original quantum state of the Big-Bang? Perhaps all we see is a 4D simulation of what is encoded in a smaller number of dimensions within a quantum superposition of the ‘Big-Bang’, without the expansion actually having to occur?

It is in the senses listed above that has had many theorists entertaining the possibility that timelessness could exist in our universe beyond the smearing of spacetime seen in quantum phenomenon. Julian Barbour has in fact worked to show what a ‘timeless’, fully spatialized model of the time of the universe might look like. Barbour imagines a quantum superposed state in which every possible universe that could emerge from such superposed state exists as a branch in that state, and that some of these states would include false ‘memories’ or embeddings of some states within others. Our consciousness of the world actually moving through time could simply be a flashing between these states in a way that gives the illusion of movement. Since memories are built into our sense of the world, each snapshot would feel like it had history, even if it didn’t, and even if these slices didn’t come in order. We wouldn’t in fact know the different between a random fluctuation between possible universes and linear progression, for the illusion would be there. While a reeeeeaaal stretch (and in some ways similar to Descartes’ ‘evil god’ argument), at least it seems to me, there is no way in fact to disprove such an approach.

But perhaps we don’t need to look quite this far to find examples of timelessness in our world. The simple photon can take care of that for us. Photons move at the speed of light. Since moving at the speed of light compresses spacetime, what would it be like to be a photon?

We know that as one approaches the speed of light, the world around one seems to stop moving, time slows down and screetches to a halt, and space spreads out really long in the direction of one’s movement. In fact, in one’s direction of movement, one’s sides would become so long and spread out that anything in front or behind you would start to shrink in size, until your sides become lines and eventually a blur and then sheet stretching from one’s front to one’s back. As one approaches the speed of light, one’s environment congeals, for in fact, you have, in a sense, left spacetime for timelessness.

Why then do we see photons? Because we keep smacking into them! Matter and light interact on a regular basis. As a photon smacks into matter, it adds energy to the atom it hits, and is often then kicked back out, but at a modified frequency. The angle and frequency/color of the light as it keeps being smacked around in this sense is precisely what our eyes are sensitized to read.

But what would it be like if you were timeless, like a photon, yet also sentient? Of course, we cannot know, but we can speculate. What would a photon ‘see’ of all this? Since all space is opaque to something moving at the speed of light, and since this entity moving at the speed of light exists outside of time, and since a photon is a quantum particle in which superposition of states is possible, it doesn’t seem unlikely that every interaction that the photon has with matter, and those periods outside of time, are layered one on top of the other, at the same ‘out of time’. In a sense, this spatializes time.

Of course, photons often have short lives, for a photon which hits an atom is not necessarily the same photon emitted by that atom shortly thereafter. But there is also no way to be sure that all the photons in the universe are not in fact multiple appearances of the same photon! For in fact, if any photon is outside of time, how would it appear to us, creatures within time?

We can find an analogue by imagining how a 2D line creature would sense the presence of an entity which could navigate a third dimension (something explored in many of the versions of Edwin Abbott’s Flatland). A 2D creature would see a 2D friend of theirs vanish and appear somewhere else, as if they’d jumped in and out of existence, and went missing for the time in between. But for us in the third dimension, there was no vanishing, just our 3D figure had ceased being sliced by the 2D world of the ‘flatlanders.’

So it is with a photon. If photons are truly outside of time, and have a markedly different relation to space, might it be that there is simply one photon, that jumps in and out of our spacetime, just as a 3D figure seems to jump in and out of 2D space? Some scientists think this could very well be the case. We already know that the phenomenon of ‘gravitational lensing’ allows for multiple copies to appear when gravity warps spacetime so that light rays bend around it, giving the impression to our eye that there are many copies of what is ultimately one. What if gravitational lensing has a more radical analogue at work in regard to photons, seemingly multiplying copies of one photon throughout spacetime? If gravity can make copies of images, might extreme gravity make copies of entities, particularly those which are themselves light?

This further explains why some have argued that it is possible that our whole universe is simply the illusion of movement within a superpositioned quantum state. We are simply ‘reading’ the hologram, which results in the sensation of ‘moving’ through time, in the manner described by Barbour, within quantum fluctuations in this superposed state.

Welch begins her argument by attempting to describe how it might be that time could emerge from timelessness. And she uses fractals to do this.